v=(c/2); c=1; d1=(Sqrt[((c+v)/(c-v))]); d2=(1/d1); γ=(1/(Sqrt[1-((v^2)/(c^2))])); T=2π;

p1=Manipulate[Plot[{Sin[x+c t], Sin[x-c t], Sin[x+c t]+Sin[x-c t], 2Sin[x],2Sin[x+π]},{x,0,4π}, Frame->True, PlotRange->{{0,4π},{-2,2}}, GridLines->{{π,2π,3π},{}}, PlotStyle->{{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Gray, Dashed}, {Gray, Dashed}},FrameTicks->{{{-1,0,1},None},{{0,π,2π,3π},None}}],{t,0,T}]

p2=Manipulate[Plot[{Sin[d1 x+c τ/γ], Sin[d2 x-c τ/γ], Sin[d1 x+c τ/γ]+Sin[d2 x-c τ/γ], 2Sin[x*γ], 2Sin[π+x*γ]},{x,0,4π/γ}, Frame->True, PlotRange->{{0,4π/γ},{-2,2}}, GridLines->{{π/γ, 2π/γ, 3π/γ},{}}, PlotStyle->{{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Gray, Dashed}, {Gray, Dashed}},FrameTicks->{{{-1,0,1},None},{{0,N[π/γ,6],N[2π/γ,6],N[3π/γ,6]},None}}],{τ,0,T γ}]

p3=Manipulate[Plot[{Sin[d1 x+c т d1], Sin[d2 x-c т d2], Sin[d1 x+c т d1]+Sin[d2 x-c т d2], 2Sin[x*γ+c т d2], 2Sin[π+x*γ+c т d2]},{x,0,4π/γ}, Frame->True, PlotRange->{{0,4π/γ},{-2,2}}, GridLines->{Table[n π/γ-v т,{n,1,12}],{}}, PlotStyle->{{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Gray, Dashed}, {Gray, Dashed}},FrameTicks->{{{-1,0,1},None},{{0,N[π/γ,6],N[2π/γ,6],N[3π/γ,6]},None}}],{т,0,2T/γ}]

Export["plot1.avi", p1, "FrameRate"->200]

Export["plot2.avi", p2, "FrameRate"->200]

Export["plot3.avi", p3, "FrameRate"->200]